Surface segregation amplification in miscible polymer blends near criticality

– In atomic, small molecule or polymeric multicomponent materials, surface compositions naturally differ from the bulk because one component (or phase) will generally favor the surface region. Binary polymer blends represent a model system to investigate surface enrichment because segregation is enhanced by the small combinatorial entropy of mixing and amplified by chain connectivity (relative to small-molecule systems). Therefore, polymers are advantageous systems for probing the thermodynamic complexities underlying surface enrichment in mixtures. In this work, the surface excess of binary polymer blends is studied as a function of composition and temperature in the vicinity of the critical point. Although the surface excess away from criticality behaves as anticipated, it is found to grow slower than expected as criticality is approached from the one-phase region. These results suggest that the surface and bulk thermodynamics are coupled. Coatings, paints and adhesives are just a few examples where surface composition plays a critical role. More specifically, the surface of a miscible blend of two liquids (A/B) typically has a composition that differs from the bulk because the component with the lower surface free energy (e.g., A) tends to segregate to the surface to minimize the total free energy of the system. The volume fraction profile of A decays monotonically from the surface to the bulk over a distance comparable to the correlation length, ξ [1]. Upon approaching the critical solution point from the one-phase region, ξ increases strongly and correspondingly the surface layer thickness grows. Indeed, the surface excess of A in A/B liquid mixtures has been found to increase rapidly as the critical temperature is approached [2], [3]. Theoretically, the total free energy of the mixture is determined simply by summing the bulk and surface free energies, F = Fb + Fs, where Fb and Fs are assumed to be independent [4]. The Fb term contains the free energy of a homogeneous mixture plus a contribution due to the volume fraction gradients. While bulk thermodynamics of binary blends is fairly well understood, a fundamental description of Fs is presently lacking. Before phenomena such as wetting transitions can be () Present address: Department of Materials Science and Engineering, Cornell University, Ithaca, NY 14853, USA. () E-mail: [email protected] c © Les Editions de Physique 172 EUROPHYSICS LETTERS accurately described, several outstanding issues regarding Fs must be understood, such as the range of the surface-liquid interactions, the functional form of Fs, and the interdependence between Fb and Fs. Polymer blends (mixtures) represent model systems for studying surface segregation. One reason is that the bulk thermodynamics of polymer blends can be successfully treated by a mean-field approach over a broader range of temperature than low-molecular-weight species. Secondly, due to chain connectivity, correlation lengths in polymer blends are much larger than in small-molecule liquids. Hence, even far from the critical solution point, the surface excess in polymer blends is large and thus readily observed experimentally [5]. Moreover, in the vicinity of the critical point, polymer blends may reveal surface segregation behavior not previously observed in small-molecule liquids. Using miscible blends of deuterated polystyrene (dPS) and poly(styrene-co-4-bromostyrene), we show that the surface excess of dPS, z∗, is a maximum near a dPS bulk volume fraction, φ∞, of 0.50. At constant φ∞, z ∗ is found to increase as the temperature is lowered towards the critical temperature. However, this increase is not as strong as that predicted by assuming that Fb and Fs are independent. We suggest that the “suppression” of z∗ results from a coupling between Fb and Fs. Schmidt and Binder (SB) extended Cahn’s treatment to describe surface enrichment of A from an A/B polymer blend [6]. Surface-polymer interactions were modeled as short-ranged so that only polymer segments adjacent to the surface contributed to Fs. Thus Fs depended on the surface volume fraction of A, φ1. The “strength” of Fs was mainly determined by the difference between the A and B surface energies. Although this model accurately described experiments carried out at temperatures far from the critical temperature, Tc [5], recent experiments [7], [8] and calculations [9] indicated that the SB form of Fs is insufficient to describe experiments where φ1 approaches 1. By including a surface entropy contribution, Cohen and Muthukumar (CM) were able to account for this deviation of Fs near φ1 = 1 [10]. To further improve the description of Fs, CM considered the effects of the volume fraction gradients evaluated at the surface which accounted for the different response of polymer chains near the surface, relative to the bulk, towards composition fluctuations. Recently, Brazhnik, Freed and Tang (BFT) expanded upon this idea by including the influence of chain connectivity and local correlations on Fs [11]. One may expect these contributions to Fs to be particularly important in the vicinity of Tc. While the SB and CM models treated Fb and Fs as two independent terms, the BFT theory includes a coupling between the bulk and surface free energies. In this letter, we will provide the experimental evidence for coupling between Fb and Fs. The system under investigation was a miscible blend of deuterated polystyrene, dPS, and a statistical copolymer poly(styrene-co-4-bromostyrene), PBrS, with 0.080 mole fraction of the 4-bromostyrene, BrS, units. The numbers of segments of dPS and PBrS were 1650 and 1670, respectively. The copolymer was prepared by brominating polystyrene following the procedure by Kambour, Bendler and Bopp [12] and its bromine content was determined by elemental analysis. Blends of dPS and PBrS represent a model system because the Flory-Huggins interaction parameters, χ, can be tuned by simply varying the content of BrS in the copolymer. In this way, Tc can be precisely adjusted. Moreover, having a lower surface energy than PBrS, dPS partitions preferentially at the surface [13]. To prepare thin films, the toluene solutions of dPS and PBrS were then spin-coated on silicon wafers previously etched in a HF/water bath. Samples were dried in a vacuum oven at 90 ◦C. Film thicknesses measured by ellipsometry ranged from 220 to 250 nm about 20 to 23 times the bulk radius of gyration of dPS. Samples were annealed under vacuum at either 222, 207, 200 or 195 ◦C. To ensure equilibrium, annealing times were chosen such that the ratio of diffusion distance to sample thickness, 2 √ Dt/L, was always larger than 15. The diffusion time t ranged from 4 to 6 days. D is the mutual diffusion coefficient. The volume fraction profiles j. genzer et al.: surface segregation amplification in miscible etc. 173 Fig. 1. – Surface excess of dPS, z, determined using LE-FRES at 195 (solid circles), 200 (open circles), 207 (solid squares), and 222 C (open squares) for mixtures with various φ∞. The error bars represent the experimental uncertainty in z. The solid lines are guides to the eye. of dPS were measured by low-energy forward recoil spectrometry (LE-FRES) [14]. The depth resolution of LE-FRES was about 40 nm near the sample surface. LE-FRES provided a direct measure of the dPS surface excess, z∗, independent of any model. The coexistence for the dPS/PBrS system was determined from the Flory-Huggins theory using χ’s obtained by interpolating values for dPS/PBrS couples with various BrS mole fractions [15], [16]. The critical point is located at a φ∞ of 0.502 and a temperature of 189 ◦C. To check the accuracy of the calculated phase diagram, bilayers of dPS and PBrS were annealed at 160, 170 and 180 ◦C and the polymer volume fractions at the coexistence were measured by LE-FRES [16], [17]. The agreement between the calculated and measured coexisting phases was very good. At all temperatures studied, the dPS/PBrS system was in the mean-field regime. The crossover between the mean-field and critical regimes was about 192 ◦C, as determined from the conditions given in ref. [18]. Figure 1 shows that z∗ increases as φ∞ increases, reaches a maximum near φ∞ ∼ 0.5 and then decreases as φ∞ goes to 1. This behavior has been observed previously [16]. More importantly, fig. 1 demonstrates that z∗ increases very rapidly as T approaches Tc. For example, near φ∞ ∼ 0.5 z∗ increases by a factor of 2 as T decreases from 222 to 195 ◦C. This trend is expected if one recalls that z∗ scales with the correlation length, ξ. Because ξ increases as T approaches Tc [19], z ∗ will correspondingly increase upon lowering T as observed in fig. 1. To our knowledge, these experiments represent the most complete study of the temperature dependence of z∗ near Tc. Figure 1 reveals two significant differences between surface segregation in small-molecule mixtures and polymer blends. First, for dPS/PBrS the ∆T = T − Tc at which z∗ rapidly increases is about 30 ◦C, whereas ∆T is only about 4 ◦C for mixtures of heptane and nitrobenzene [3]. Second, being amplified by chain connectivity, z∗ for polymer blends is typically an order of magnitude larger than in small molecules [20]. Knowing z∗, Fs can be evaluated. Recently, Norton and coworkers recognized that at constant temperature z∗ is related to the surface energy, γ, via the Gibbs adsorption equation [8]: